Counting and Sampling Minimum Cuts in Genus g Graphs

Let \(G\) be a directed graph with \(n\) vertices embedded on an orientable surface of genus \(g\) with two designated vertices \(s\) and \(t\) . We show that computing the number of minimum \((s,t)\) -cuts in \(G\) is fixed-parameter tractable in \(g\) . Specifically, we give a \(2^{O(g)} n^2\) time algorithm for this problem. Our algorithm requires counting sets of cycles in a particular integer homology class. That we can count these cycles is an interesting result in itself as there are no prior results that are fixed-parameter tractable and deal directly with integer homology. We also describe an algorithm which, after running our algorithm to count minimum cuts once, can sample an \((s,t)\) -minimum cut uniformly at random in \(O(n \log n)\) time per sample.     

Die Bildung von Dampfkeimen im Blasensieden

Zusammenfassung Die begrifflichen Grundlagen zweier zur Zeit weitestens akzeptierter Analysen der Dampfphasenkeimbildung werden untersucht. Beide nehmen an, daß ein Druckgleichgewicht für die Bildung stabiler Keime kritisch ist. Da vor kurzem gezeigt worden ist, daß die Idee eines Druckunterschiedes zwischen den zwei Seiten einer gekrümmten Grenzfläche Fehler einschließt, ist eine neue Analyse erforderlich. Die Keimbildung wird als ein von einer Freien-Energie-Barriere bestimmter Vorgang formuliert. Kritische Radien für stabile Keime und Dampfdrucke in Bläschen werden als Funktion der Überhitzung für Wasser berechnet.

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The formation of vapor phase nuclei in nucleate boiling

The conceptual bases of two analyses of vapor phase nucleation that share wide current acceptance are examined. Both consider a balance of pressure to be critical to the formation of stable nuclei. Because the concept of a pressure difference across curved interfaces has recently been shown faulty, a new analysis is required. Nucleation is formulated as a process governed by a free energy barrier. Critical radii for stable nuclei and vapor pressure in bubbles are calculated for water as functions of superheating.

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Herrn Prof. Dr.H. Nowotny gewidmet.

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Diese Arbeit wurde von dem Metallurgy and Materials Branch der United States Atomic Energy Commission unterstützt. Eine englische Übersetzung ist als University of California Radiation Laboratory Report UCRL-20552 erhältlich.     

Probing electronic effects in the asymmetric Heck reaction with the BIPI ligands

[structure: see text] The new BIPI ligands are phosphinoimidazolines that can be electronically tuned in three different ligand regions to explore electronic effects in asymmetric catalysis. Their application to the asymmetric Heck reaction (AHR) in the creation of a chiral quaternary center is described. Enantioselectivity is shown for the first time to depend linearly on phosphine electron density. Changing the ligand basicity by variation of the R(2) or R(3) substituents reverses facial selectivity.     

Ruthenium-catalyzed decarboxylative allylation of nonstabilized ketone enolates

[reaction: see text] Bipyridyl(pentamethylcyclopentadienyl)ruthenium chloride is an efficient catalyst for the formal [3,3] rearrangement of allyl beta-ketoesters. The mechanism of the transformation involves formation of pi-allyl ruthenium intermediates, which are selectively attacked at the more substituted allyl terminus by freely diffusing enolates. Decarboxylation of beta-ketocarboxylates allows generation of enolates under extremely mild conditions.     

Synthesis of unsymmetrically substituted 1,3-butadiynes and 1,3,5-hexatriynes via alkylidene carbenoid rearrangements

Unsymmetrically substituted 1,3-butadiynes and 1,3,5-hexatriynes are synthesized in four steps from commercially available aldehydes or carboxylic acids. The key step in this process involves a Fritsch-Buttenberg-Wiechell rearrangement, in which an alkylidene carbenoid intermediate subsequently rearranges to the desired polyyne. This rearrangement proceeds under mild conditions, and it is tolerant of a range of functionalities. In general, the procedurally facile formation of the dibromoolefinic precursors, in combination with the effectiveness of the rearrangement step, makes this procedure an attractive alternative to traditional methods for di- and triyne synthesis that utilize palladium or copper catalysis.     

Ene-diamine versus imine-amine isomeric preferences

Cyanide-catalyzed aldimine coupling was employed to synthesize compounds with 1,2-ene-diamine and alpha-imine-amine structural motifs: 1,2,N,N'-tetraphenyletheylene-1,2-diamine (13) and (+/-)-2,3-di-(2-hydroxyphenyl)-1,2-dihydroquinoxaline (17), respectively. Single-crystal X-ray diffraction provided solid-state structures and density functional theory calculations were used to probe isomeric preferences within this and the related hydroxy-ketone/ene-diol system. The ene-diamine and imine-amine core structures were calculated (B3LYP/6-311++G(d,p)) to be essentially identical in energy (DeltaG = 0.2 kcal/mol in favor of the imine-amine, within the error of the calculation). However, additional effects-such as pi conjugation-in 13 render an ene-diamine structure that is slightly more stable than the imine-amine tautomer (14) (DeltaG = 0.2-0.7 kcal/mol, within the error of the calculation). In contrast, the intramolecular hydrogen bonding present in 17 significantly favors the imine-amine isomer over the ene-diamine tautomer (18) (DeltaG = 7.2-8.9 kcal/mol). For both 13 and 17, the optimized calculated structures (B3LYP/6-31+G(d')) are identical to those observed by single-crystal X-ray diffraction.     

Synthesis of unsymmetrical thioflavylium dyes from julolidine derivatives and polyfluorinated triphenyldihydropyrazoles

Unsymmetrical polymethine dyes have been synthesized from 6-tert-butyl-4-methylthioflavylium perchlorates and nitrogen-containing heterocyclic aldehydes derived from julolidine and polyfluorinated triphenyl-4,5-dihydro-1H-pyrazoles. Spectral characteristics of the obtained compounds have been studied.     

Defining near-surface groundwater flow regimes in the semi-arid glaciated plains of North America

The dominant transport mechanisms controlling the migration of contaminants in geologic media are advection and molecular diffusion. To date, defining which transport mechanism dominates in saturated, non-lithified sediments has been difficult. Here, we illustrate the value of using detailed profiles of the conservative stable isotope values of water (δ²H and δ¹⁸O) to identify the dominant processes of contaminant transport (i.e. diffusion- or advection-dominated transport) in near-surface, non-lithified, saturated sediments of the Interior Plains of North America (IPNA). The approach presented uses detailed δ¹⁸O analyses of glacial till, glaciolacustrine clay, and fluvial sand core samples taken to depths of 11–50 m below ground at 22 sites across the IPNA to show whether transport in the fractured and oxidized sediments is dominated by advection or diffusion. Diffusion is by far the dominant transport mechanism in fine-textured lacustrine and glacial till sediments, but lateral advection dominates transport in sand-rich sediments and some oxidized, fine-textured lacustrine and glacial till sediments. The approach presented has a number of applications, including identifying dominant transport mechanisms in geomedia and potential protective barriers for underlying aquifers or surface waters, constraining groundwater transport models, and selecting optimum locations for monitoring wells. These findings should be applicable to most glaciated regions of the world that are composed of similar hydrogeologic units (i.e. low K clay till layers overlain by higher K coarse-textured aquifers or weathered clay till layers) and may also be applicable to non-glaciated regions exhibiting similar hydrogeologic characteristics.     

A polymeric domain that promotes cellular internalization

Polymers have emerged as powerful biological tools; however, their ability to gain access to the intracellular environment is limited. To expand the biological utility of polymer scaffolds, we have synthesized an internalization domain using the ring-opening metathesis polymerization (ROMP). A polymer functionalized with guanidinium groups is effectively internalized by cells and localized in both vesicles and the cytoplasm. Because the synthesis of such materials is modular, we anticipate that compounds of this type can be fashioned that facilitate the delivery of cargo via end-cap derivatization or block copolymer synthesis.